Self-inscribed Regular Hyperbolic Honeycombs

  • Peter McMullen
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 234)


This paper describes ways that certain regular honeycombs of non-finite type in d-dimensional hyperbolic space \(\mathbb {H}^d\) for \(d = 2,3\) and 5 can be inscribed in others, in particular showing that some can be inscribed properly in copies of themselves.


Coxeter group Simplex dissection Hyperbolic space Regular honeycomb Self-inscribed Compound 

MSC (2010):

Primary 51M20 Secondary 51M10 


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University College LondonLondonUK

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